Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #27212897 | C2 | semidirect |
| 4. #27212896 | C2 | semidirect |
| 5. #334×C211 | C2 | semidirect |
| 25. C8×D211 | C8 | semidirect |
| 43. C211⋊C8 | C2×C8 | semidirect |
| 49. C8×C211 | C2×C8 | semidirect |
| 64. D211 | #334 | direct (N × H) |
| 65. C211 | C2×#334 | semidirect |
| 71. #334 | D211 | direct (N × H) |
| 115. C8 | C8×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊C8×D211 | 2 |
| C4×C8×D211 | 2 |
| #27212897 | 2 |
| #27212896 | 2 |
| #334×C211 | 2 |
| C2×#334 | 211 |